Yes it is a pressure reducing valve. Here is a link:
http://www.zurn.com/Pages/ProductDet...NodeKey=424788
From that link you can read over the 2 pdf files there. The spec sheet, and the install instructions.
If you open the parts diagram on the installation instructions you will see that the first brass nut (furthest right in your photo) is your "adjustment bolt". Or in other words, by tightening this bolt all you are doing is increasing the downstream pressure in the water lines. You are not fixing the leak.
This particular model (Wilkins BR4) of valve is discontinued. But parts are available. The replacement for this valve is NR3XL.
As for who is responsible I am unsure. My guess would be that anything downstream of the meter is your responsibility, but the poster above seems certain that it is the City. So best to ask the city first.
If you are responsible for the repair, You need to find a plumber and the model number above.